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Simplifying y2 + -4y + -20 = 3y + 2 Reorder the terms: -20 + -4y + y2 = 3y + 2 Reorder the terms: -20 + -4y + y2 = 2 + 3y Solving -20 + -4y + y2 = 2 + 3y Solving for variable 'y'. Reorder the terms: -20 + -2 + -4y + -3y + y2 = 2 + 3y + -2 + -3y Combine like terms: -20 + -2 = -22 -22 + -4y + -3y + y2 = 2 + 3y + -2 + -3y Combine like terms: -4y + -3y = -7y -22 + -7y + y2 = 2 + 3y + -2 + -3y Reorder the terms: -22 + -7y + y2 = 2 + -2 + 3y + -3y Combine like terms: 2 + -2 = 0 -22 + -7y + y2 = 0 + 3y + -3y -22 + -7y + y2 = 3y + -3y Combine like terms: 3y + -3y = 0 -22 + -7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -7y + 22 + y2 = 0 + 22 Reorder the terms: -22 + 22 + -7y + y2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -7y + y2 = 0 + 22 -7y + y2 = 0 + 22 Combine like terms: 0 + 22 = 22 -7y + y2 = 22 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = 22 + 12.25 Reorder the terms: 12.25 + -7y + y2 = 22 + 12.25 Combine like terms: 22 + 12.25 = 34.25 12.25 + -7y + y2 = 34.25 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (y + -3.5) equal to 5.852349955 and -5.852349955.Subproblem 1
y + -3.5 = 5.852349955 Simplifying y + -3.5 = 5.852349955 Reorder the terms: -3.5 + y = 5.852349955 Solving -3.5 + y = 5.852349955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 5.852349955 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 5.852349955 + 3.5 y = 5.852349955 + 3.5 Combine like terms: 5.852349955 + 3.5 = 9.352349955 y = 9.352349955 Simplifying y = 9.352349955Subproblem 2
y + -3.5 = -5.852349955 Simplifying y + -3.5 = -5.852349955 Reorder the terms: -3.5 + y = -5.852349955 Solving -3.5 + y = -5.852349955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -5.852349955 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -5.852349955 + 3.5 y = -5.852349955 + 3.5 Combine like terms: -5.852349955 + 3.5 = -2.352349955 y = -2.352349955 Simplifying y = -2.352349955Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.352349955, -2.352349955}
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